Question

Which of the rectangles may be used to multiply $289\times 17$ using the lattice method?

• A.
• B.
• C. (a) and (b) above.
• D. None of the above

Answer 1

The correct option is C (a) and (b) above.

• To find out the value of $289\times 17$ using the lattice method, we have to split $289$ into it's digits as $2$, $8$ and $9$, and write sequentially on top of the table from left to right.

• Whereas, we have to split $17$ into it's digits as $1$ and $7$, and write on right of the table from top to down.

Hence, to multiply $289\times 17$ we need $3\times 2$ rectangular table (as $289$ has $3$ digits and $17$ has $2$ digit) as shown in below figure,


Similarly, since $17$ has $2$ digits and $289$ has $3$ digits to find $17\times 289$ we need $2\times 3$ rectangular tables as shown in below figure,

And as we know $289\times 17=17\times 289$ (By commutative property of multiplication) therefore, both the rectangular tables $3\times 2$ and $2\times 3$ can be used to multiply $289\times 17$ by lattice method.

$\therefore$ Option (c.) is the correct one.